Learning LWF Chain Graphs: A Markov Blanket Discovery Approach

Mohammad Ali Javidian, Marco Valtorta, Pooyan Jamshidi
Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), PMLR 124:1069-1078, 2020.

Abstract

This paper provides a graphical characterization of Markov blankets in chaingraphs (CGs) under the Lauritzen-Wermuth-Frydenberg (LWF) interpretation. The characterization is different from the well-known one for Bayesian networks and generalizes it. We provide a novel scalable and sound algorithmfor Markov blanket discovery in LWF CGs and prove that the Grow-Shrink algorithm, the IAMB algorithm, and its variants are still correct for Markov blanket discovery in LWF CGs under the same assumptions as for Bayesian networks. We provide a sound and scalable constraint-based framework for learning the structure of LWF CGs from faithful causally sufficient data and prove its correctness when the Markov blanket discovery algorithms in this paper are used. Our proposed algorithms compare positively/competitively against the state-of-the-art LCD (Learn Chain graphs via Decomposition) algorithm, depending on the algorithm that is used for Markov blanket discovery. Our proposed algorithms make a broad range of inference/learning problems computationallytractable and more reliable because they exploit locality.

Cite this Paper

BibTeX
@InProceedings{pmlr-v124-ali-javidian20a, title = {Learning LWF Chain Graphs: A Markov Blanket Discovery Approach}, author = {Ali Javidian, Mohammad and Valtorta, Marco and Jamshidi, Pooyan}, booktitle = {Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI)}, pages = {1069--1078}, year = {2020}, editor = {Peters, Jonas and Sontag, David}, volume = {124}, series = {Proceedings of Machine Learning Research}, month = {03--06 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v124/ali-javidian20a/ali-javidian20a.pdf}, url = {https://proceedings.mlr.press/v124/ali-javidian20a.html}, abstract = {This paper provides a graphical characterization of Markov blankets in chaingraphs (CGs) under the Lauritzen-Wermuth-Frydenberg (LWF) interpretation. The characterization is different from the well-known one for Bayesian networks and generalizes it. We provide a novel scalable and sound algorithmfor Markov blanket discovery in LWF CGs and prove that the Grow-Shrink algorithm, the IAMB algorithm, and its variants are still correct for Markov blanket discovery in LWF CGs under the same assumptions as for Bayesian networks. We provide a sound and scalable constraint-based framework for learning the structure of LWF CGs from faithful causally sufficient data and prove its correctness when the Markov blanket discovery algorithms in this paper are used. Our proposed algorithms compare positively/competitively against the state-of-the-art LCD (Learn Chain graphs via Decomposition) algorithm, depending on the algorithm that is used for Markov blanket discovery. Our proposed algorithms make a broad range of inference/learning problems computationallytractable and more reliable because they exploit locality.} }
Endnote
%0 Conference Paper %T Learning LWF Chain Graphs: A Markov Blanket Discovery Approach %A Mohammad Ali Javidian %A Marco Valtorta %A Pooyan Jamshidi %B Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI) %C Proceedings of Machine Learning Research %D 2020 %E Jonas Peters %E David Sontag %F pmlr-v124-ali-javidian20a %I PMLR %P 1069--1078 %U https://proceedings.mlr.press/v124/ali-javidian20a.html %V 124 %X This paper provides a graphical characterization of Markov blankets in chaingraphs (CGs) under the Lauritzen-Wermuth-Frydenberg (LWF) interpretation. The characterization is different from the well-known one for Bayesian networks and generalizes it. We provide a novel scalable and sound algorithmfor Markov blanket discovery in LWF CGs and prove that the Grow-Shrink algorithm, the IAMB algorithm, and its variants are still correct for Markov blanket discovery in LWF CGs under the same assumptions as for Bayesian networks. We provide a sound and scalable constraint-based framework for learning the structure of LWF CGs from faithful causally sufficient data and prove its correctness when the Markov blanket discovery algorithms in this paper are used. Our proposed algorithms compare positively/competitively against the state-of-the-art LCD (Learn Chain graphs via Decomposition) algorithm, depending on the algorithm that is used for Markov blanket discovery. Our proposed algorithms make a broad range of inference/learning problems computationallytractable and more reliable because they exploit locality.
APA
Ali Javidian, M., Valtorta, M. & Jamshidi, P.. (2020). Learning LWF Chain Graphs: A Markov Blanket Discovery Approach. Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), in Proceedings of Machine Learning Research 124:1069-1078 Available from https://proceedings.mlr.press/v124/ali-javidian20a.html.

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